# On approximating operators preserving certain polynomials

## Abstract

The paper centers around a general class of discrete linear positive operators depending on a real parameter $$\alpha \geq 0$$ and preserving both the constants and the polynomial $$x^{2}+\alpha x$$. Under some given conditions, this sequence of operators forms an approximation process for certain real valued functions defined on an interval $$J$$. Two cases are investigated: $$J=[0,1]$$ and $$J=$$$$[0,\infty )$$, respectively. Quantitative estimates are proved in different normed spaces and some particular cases are presented.

## Authors

Octavian Agratini
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

Faculty of Sciences, Tishrin University, 1267 Latakia, Syria

## Keywords

positive linear operators, Popoviciu-Bohman-Korovkin criterion, Bernstein polynomials, Szasz-Mirakjan operators, Baskakov operators, polynomial weight spaces

## Paper coordinates

O. Agratini, S. Tarabie, On approximating operators preserving certain polynomials, Automation, Computers, Applied Mathematics, 17 (2008) no. 2, pp. 191-199

## PDF

##### Journal

Automation Computers Applied Mathematics

http://acam.tucn.ro/HTML/INDEX.HTM

1221–437X